This invention describes a set of machines, and a structural system capable of building structures by the additive assembly of discrete parts. These digital material assemblies (described, in part, in U.S. Pat. No. 7,848,838, US20120094060, WO2014025944, US20140302261, US20140300211) constrain the constituent parts to a discrete set of possible positions and orientations. In doing so, the structures exhibit many of the properties inherent in digital communication such as error correction, fault tolerance and allow the assembly of precise structures with comparatively imprecise tools. The machines responsible for assembling digital materials should leverage, to the extent possible, the interlocking and error-correction naturally present in the discrete parts.